Four-Dimensional Manifolds and Projective Structure may be considered first as an introduction to differential geometry and, in particular, to 4−dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds. The initial chapters mainly cover the elementary aspects of set theory, linear algebra, topology, Euclidean geometry, manifold theory and differential geometry, including the idea of a metric and a connection on a manifold and the concept of curvature. After this, the author dives deeper into 4-dimensional manifolds and, in particular, the positive definite case for the metric. The book also covers Lorentz signature and neutral signature in detail and introduces, and makes use of, the holonomy group of such a manifold for connections associated with metrics of each of these three possible signatures. A brief interlude on some key aspects of geometrical symmetry precedes a detailed description of projective relatedness, that is, the relationship between two symmetric connections (and between their associated metrics) which give rise to the same geodesic paths. Features: Offers a detailed, straightforward discussion of the basic properties of (4-dimensional) manifolds. Introduces holonomy theory, and makes use of it, in a novel manner. Suitable for postgraduates and researchers, including master’s and PhD students.
Winner of the BAAL Book Prize 2012 Routledge Introductions to Applied Linguistics is a series of introductory level textbooks covering the core topics in Applied Linguistics, primarily designed for those entering postgraduate studies and language professionals returning to academic study. The books take an innovative "practice to theory" approach, with a 'back-to-front' structure. This leads the reader from real-world problems and issues, through a discussion of intervention and how to engage with these concerns, before finally relating these practical issues to theoretical foundations. Additional features include tasks with commentaries, a glossary of key terms, and an annotated further reading section. Exploring English Language Teaching provides a single volume introduction to the field of ELT from an applied linguistics perspective. The book addresses four central themes within English language teaching: ‘Classroom interaction and management’; ‘Method, Postmethod and methodology’; ‘Learners’; and the ‘Institutional frameworks and social contexts’ of ELT. For each, the book identifies key dilemmas and practices, examines how teachers and other language teaching professionals might intervene and deal with these concerns, and explores how such issues link to and inform applied linguistic theory. Exploring English Language Teaching is an indispensable textbook for language teachers, and for post-graduate/graduate students and advanced undergraduates studying in the areas of Applied Linguistics, Language Teacher Education, and ELT/TESOL.
Happiness and success start with becoming clear about who are you are, and establishing your authentic identity-- inside yourself, and then beyond yourself. Graham shows you who it's so hard to know yourself-- and how to do it anyway.
Environmental Law & Policy: Nature, Law & Society is a coursebook designed to access the law of environmental protection through a “taxonomic” approach, exploring the range of legal structures and legal methodologies of the field—rather than simply designing it according to air, water, toxics, etc. as subject media (which often results in duplicative legal coverage). All the major subject areas of pollution and resource conservation are covered, but they are covered according to the legal approaches they represent. The book is “Saxist,” because it originally arose and continues to carry on themes from the teaching, guidance, and writings of the late Joseph Sax, the eminent pioneer of the environment law field who emphasized the interaction between common law and public law statutory structures, and introduced the public trust doctrine as a thread undergirding and running through the entire field of environmental law. Key Features: Includes teaching analysis of the completely-revised Toxics Substances Control Act by co-author Robert Graham, Esq. of Jenner & Block who is advising corporate clients on the new law. Coverage of the Dec 2015 Paris COP-21 climate agreement in its several different aspects, incorporating analysis by coauthor Prof David Wirth who played an active role in international preparations for the Paris accord. Expanded material on carbon pricing, until recently widely thought to be a politically impossible alternative avenue for mitigation of global climate disruption. Tracking major recent revisions in toxic substance regulation, with essential comparisons to the current European model of market access chemical regulation. An updated guide through the complexities of tensions between private property rights and environmental protections, and an innovative clarification of recent Supreme Court caselaw. An innovative chapter on official “planning”— a basic and problematic element of environmental governance, whether at the local level or national public lands level. The purchase of this Kindle edition does not entitle you to receive 1-year FREE digital access to the corresponding Examples & Explanations in your course area. In order to receive access to the hypothetical questions complemented by detailed explanations found in the Examples & Explanations, you will need to purchase a new print casebook.
This book contains eight papers from a detailed study of technical college provision in KwaZulu-Natal, South Africa, that raised the following four issues relevant to the transformation of technical colleges across South Africa: (1) the teaching and learning environment at technical colleges is suboptimal; (2) social relations at the technical colleges are tense, with few institutions having successfully come to terms with the rapid deracialization of student enrollments in recent years; (3) the labor market surrounding technical colleges appears totally dysfunctional, with few students obtaining employment after technical college training; and (4) the separate development policies of the past necessitate institutional restructuring. The following papers are included: "A Study of Technical Colleges in KwaZulu-Natal: A Methodological Introduction" (Andre Kraak, Graham Hall); "Problems Facing Further Education and Training" (Andre Kraak); "Planning Imperative: New Policy Framework in FET [Further Education and Training]" (Andre Kraak); "Socio-Economic and Educational Profile of KwaZulu-Natal" (Nisaar Mahomed); "Quantitative Overview of the Technical Colleges of KwaZulu-Natal" (Graham Hall); "Learning, Teaching and Management Environment: Evidence from Qualitative Studies" (Andre Kraak); "Autonomy and Responsiveness: Evidence from the Qualitative Case Studies" (Andre Kraak); and "Critical Overview: The Need for Labour Market and Institutional Reform" (Andre Kraak). The bibliography contains 52 references. (MN)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.